Chapter 10, Problem 10.3.15P

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347

Chapter
Section

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

A propped cantilever beam is subjected to uniform load q. The beam has flexural rigidity EI = 2000 kip-ft2 and the length of the beam is 10 ft. Find the intensity q of the distributed load if the maximum displacement of the beam is δ max = 0.125 in.

To determine

Intensity of distributed load

Explanation

Given Information:

The following figure is given along with relevant information,

Also EI=2000Â kip-ft2,Â L=10Â ft,Â Î´max=0.125Â in.

Calculation:

Consider the following free body diagram,

Take equilibrium of forces in vertical as,

âˆ‘Fy=0â‡’RA+RB=qLÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(1)

Take equilibrium of moments about A as,

âˆ‘MA=0â‡’MA+RBLâˆ’qL2/2=0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ....(2)

The shear force at distance x from point A is given by,

V=RAâˆ’qx

The bending moment at distance x from point A is given by,

â€ƒâ€ƒM=âˆ’MA+RAxâˆ’qx2/2

The deflection and bending moment is related by following differential equation

d2vdx2=MEIÂ Â Â Â Â Â Â Â Â Â ...

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